7/2x+1/2x=10.5+9.25x

Solution for 7/2x+1/2x=10.5+9.25x equation:

7/2x+1/2x=10.5+9.25x

We move all terms to the left:

7/2x+1/2x-(10.5+9.25x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x+1/2x-(9.25x+10.5)=0

We get rid of parentheses

7/2x+1/2x-9.25x-10.5=0

We multiply all the terms by the denominator


-(9.25x)*2x-(10.5)*2x+7+1=0

We add all the numbers together, and all the variables

-(+9.25x)*2x-(10.5)*2x+7+1=0

We add all the numbers together, and all the variables

-(+9.25x)*2x-(10.5)*2x+8=0

We multiply parentheses

-18x^2-21x+8=0

a = -18; b = -21; c = +8;
Δ = b2-4ac
Δ = -212-4·(-18)·8
Δ = 1017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1017}=\sqrt{9*113}=\sqrt{9}*\sqrt{113}=3\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{113}}{2*-18}=\frac{21-3\sqrt{113}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{113}}{2*-18}=\frac{21+3\sqrt{113}}{-36}
$